Homogeneous nearly Kähler manifolds

Abstract

The structure of nearly Kähler manifolds was studied by Gray in several articles, mainly in Gray (Math Ann 223:233–248, 1976). More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a complete strict nearly Kähler manifold is locally a Riemannian product of homogeneous nearly Kähler spaces, twistor spaces over quaternionic Kähler manifolds and six-dimensional (6D) nearly Kähler manifolds, where the homogeneous nearly Kähler factors are also 3-symmetric spaces. In the present article, we show some further properties relative to the structure of nearly Kähler manifolds and, using the lists of 3-symmetric spaces given by Wolf and Gray, we display the exhaustive list of irreducible simply connected homogeneous strict nearly Kähler manifolds. For such manifolds, we give details relative to the intrinsic torsion and the Riemannian curvature.